Evaluating the Derivative of an Inverse Function In Exercises 63-70, verify that f has an inverse function. Then use the function f and the given real number a to find
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Chapter 5 Solutions
Calculus of a Single Variable
- Explain how to find the inverse of a function from its equation. Use an example to demonstrate the steps.arrow_forwardCan a function be its own inverse? Explain.arrow_forwardFind the inverse function of f(x) = /8-a- 5. Specify the domain for f-1(x) f- (2) = Domain of f-(x) using interval notation: Check Answerarrow_forward
- Verify the inverse function theorem of y=sqrt(x+2)arrow_forwardOne model for the ideal body weight W for men (in kilograms) as a function of height h (in inches) is given by the function W(h) = 50 + 2.3(h - 60)(a) What is the ideal weight of a 6-foot male?(b) Express the height h as a function of weight W.(c) Verify that h = h(W) is the inverse of W = W(h) byshowing that h(W(h) ) = h and W(h(W) ) = W.(d) What is the height of a male who is at his ideal weight of 80 kilograms?[Note: The ideal body weight W for women (in kilograms) as a function of height h (in inches) is given by W(h) = 45.5 + 2.3(h - 60).]arrow_forwardFind the inverse function of f (x)= 4x, Verify that both 1) f (f-1(x) 2) f-1(f(x) are equal to the identity function Find the inverse function of f (x)= 1/5x, Verify that both 3) f(f-1(x) 4) f-1(f(x) are equal to the identity functionarrow_forward
- The graph of a constant f(x)= c for any constant is c is a horizontal line through the point (0,C) does a constant function have an inverse does it have an inverse function explainarrow_forwardFind the inverse function of f. f(x) = 3x3 + 9 f-(x) =arrow_forwardDetermine whether f(x) and g(x) are inverse functions of each other. f(x)= cube root of (x+2) g(x)= x^3 -2arrow_forward
- Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage